COMSOL 6.4 - Piezomagnetic Cell Rover

A conventional antenna relies on electromagnetic resonance, which means that it must be of a size comparable to the electromagnetic wavelength. This has been a difficulty for the development of smaller, millimeter-sized antennas. This tutorial is intended to show how to model a miniaturized magnetostrictive antenna developed for operating inside living cells, based on the so-called Cell Rover design presented in Ref. 1.

The Cell Rover antenna is ideal for operating inside living systems because of its small size and its relatively low resonance frequency at around 4.5 MHz. To understand the effect of mass loading and viscous damping, the device is studied in air. By exiting the antenna with an AC magnetic field applied along its length, the stress of the antenna, the magnetic flux density, the current density, and the displacement of the tip of the device are investigated.

Model Definition

The geometry of the Cell Rover is shown in Figure 1. The model is solved in 3D, and consists of a magnetostrictive antenna made of metglas placed inside a cylinder filled with air. The antenna is excited using a uniform magnetic background field. A relatively fine mesh is used for the antenna, while a coarser mesh is used for the surrounding cylinder. The computational mesh can be seen in Figure 2.

Figure 1: The model geometry.

Figure 2: The mesh used in the model.

The implementation makes use of a predefined multiphysics interface available in COMSOL, called Piezomagnetism. Selecting this interface in the Model Wizard adds the Structural Mechanics and Magnetic Fields interfaces together with the corresponding multiphysics coupling feature, Piezomagnetism.

Parameters

The model uses parameters for the excitation, the quality factor, and the metglas material properties, as given in Table 1. The properties of air are taken from the built-in COMSOL material library.

Table 1: Model parameters.
Name	Value	Description
E	152e9[Pa]	Young's modulus
nu	0.22	Poisson's ratio
d	1.19e-8[m/A]	Magnetostrictivity
sigma	7.25e5[S/m]	Conductivity
mu	300	Relative permeability
rho	7900[kg/m^3]	Density
Hac	3[Oe]	Magnetic field
Q	497	Quality factor

Results and Discussion

Two studies are performed: a Frequency Domain study and an Adaptive Frequency Sweep study. The plots shown in Figures 3-5 show the solution from the Frequency Domain study at the resonance frequency of 4.535 MHz, while Figure 6 compares the solutions from both studies.

Figure 3 shows the magnetic flux density norm and the magnetic flux density streamlines in a slice of the antenna.

Figure 4 shows the volume plot of the stress distribution in the antenna.

Figure 5 displays the volume plot of the current density norm in the antenna.

Figure 6 compares the resulting tip displacements of the first and the second study. The Adaptive Frequency Sweep study has a higher resolution output than the Frequency Domain study. The maximum displacement occurs at the resonance frequency of 4.535 MHz and has a value of 17.1 nm.

Figure 3: Magnetic flux density norm at f = 4.535 MHz.

Figure 4: Stress distribution at f = 4.535 MHz.

Figure 5: Current density norm at f = 4.535 MHz.

Figure 6: The tip displacement versus frequency for the Frequency Domain study and the Adaptive Frequency Sweep study.

Reference

1. B. Joy, Y. Cai, D.C. Bono, and others, “Cell Rover — a miniaturized magnetostrictive antenna for wireless operation inside living cells,” Nat. Commun., vol. 13, p. 5210, 2022.

Article available at: www.nature.com/articles/s41467-022-32862-4.
This source is licensed under the Creative Commons Attribution 4.0 International License: creativecommons.org/licenses/by/4.0/.
The Piezomagnetic Cell Rover tutorial model uses the device dimensions and material properties of Metglas® 2826 MB as given by the article, and the magnetic field strength and quality factor are as given for the studies done in air. The model reproduces the resonance frequency in air, as obtained from the article.

ACDC_Module/Electromagnetics_and_Mechanics/piezomagnetic_cell_rover

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file piezomagnetic_cell_rover_parameters.txt.

The imported parameters are used for the excitation, the quality factor, and the metglas material properties.

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Cell Rover

In the toolbar, click

In the window for , type Cell Rover in the text field.

Locate the section. In the text field, type 0.5.

In the text field, type 0.2.

In the text field, type 0.028.

Locate the section. From the list, choose .

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	0.25

Find the subsection. Select the checkbox.

Clear the checkbox.

Locate the section. Select the checkbox.

Click

Cylinder 1 (cyl1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 2.

Locate the section. In the text field, type -1.

Locate the section. Select the checkbox.

Click

Form Union (fin)

In the window, click .

In the window for , click

Air

In the toolbar, click

and choose .

In the window for , type Air in the text field.

Locate the section. Click

In the dialog, select in the list.

Click .

Exterior Boundaries

In the toolbar, click

and choose .

In the window for , type Exterior Boundaries in the text field.

Locate the section. Click

In the dialog, select in the list.

Click .

In the toolbar, click

Click the

button in the toolbar.

Click the

button in the toolbar.

In the window, click .

Definitions

Next, create a selection for a point of interest that can used for the stored solution later.

Explicit 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Click

In the dialog, type 3 in the text field.

Click .

Integration 1 (intop1)

In the window, expand the node.

Right-click and choose > .

In the window for , locate the section.

From the list, choose .

Select Point 3 only.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Materials

Metglas

In the window, under right-click and choose .

In the window for , type Metglas in the text field.

Locate the section. From the list, choose .

Click to expand the section. In the tree, select > > .

Click

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Young’s modulus	E	root.E	Pa	Young’s modulus and Poisson’s ratio
Poisson’s ratio	nu	root.nu	1	Young’s modulus and Poisson’s ratio
Electric conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	sigma	S/m	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic
Compliance matrix, Voigt notation	{sH11, sH12, sH22, sH13, sH23, sH33, sH14, sH24, sH34, sH44, sH15, sH25, sH35, sH45, sH55, sH16, sH26, sH36, sH46, sH56, sH66} ; sHij = sHji	{1/E, -nu/E, 1/E, -nu/E, -nu/E, 1/E, 0, 0, 0, (1+nu)/E, 0, 0, 0, 0, (1+nu)/E, 0, 0, 0, 0, 0, (1+nu)/E}	1/Pa	Strain-magnetization form
Piezomagnetic coupling matrix, Voigt notation	{dHT11, dHT21, dHT31, dHT12, dHT22, dHT32, dHT13, dHT23, dHT33, dHT14, dHT24, dHT34, dHT15, dHT25, dHT35, dHT16, dHT26, dHT36}	{d, 0, 0, 0, d, 0, 0, 0, d, 0, 0, 0, 0, 0, 0, 0, 0, 0}	m/A	Strain-magnetization form
Relative permeability	murT_iso ; murTii = murT_iso, murTij = 0	mu	1	Strain-magnetization form
Density	rho	root.rho	kg/m³	Basic